Finite Group Databasebeta

← #14453708

Subgroups — #14453708

Order 1920.

988 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×C5×D4×Q8C211yesmaximal, characteristic, complemented
2C2×#91831C211yesmaximal, characteristic, complemented
3C22×#6717C211yesmaximal, characteristic, complemented
4#11756309C211yesmaximal, characteristic
5#11751329C211yesmaximal, characteristic, complemented
6#11751328C211yesmaximal, characteristic, complemented
7#11751187C211yesmaximal, characteristic, complemented
8#11751184C211yesmaximal, characteristic, complemented
9#11751152C211yesmaximal, characteristic, complemented
10#11751150C211yesmaximal, characteristic, complemented
11#11751148C211yesmaximal, characteristic, complemented
12#11751147C211yesmaximal, characteristic, complemented
13#11751129C211yesmaximal, characteristic, complemented
14#11751127C211yesmaximal, characteristic, complemented
15#11751112C211yesmaximal, characteristic, complemented
16#10615290—31nomaximal, Hall
17C22×C3×C5×Q8C2211yescharacteristic
18C22×C3×C5×Q8C2211yescharacteristic, complemented
19C2×#6817C2211yescharacteristic
20C22×D60C2211yescharacteristic
21C3×C5×C4⋊Q8—21no—
22C3×C5×C4⋊Q8C2211yescharacteristic, complemented
23C3×C5×C22⋊Q8—21no—
24C3×C5×C22⋊Q8—21no—
25C3×C5×C22⋊Q8C2211yescharacteristic
26C3×C5×C22⋊Q8C2211yescharacteristic, complemented
27C3×C4×C5×Q8C2211yescharacteristic, complemented
28C3×C4×C5×D4—21no—
29C3×C4×C5×D4C2211yescharacteristic
30C2×#6718C2211yescharacteristic, complemented
31C2×#6718C2211yescharacteristic, complemented
32C2×#6718C2211yescharacteristic, complemented
33#91831—24no—
34C2×#6717—24no—
35C2×#6717C2211yescharacteristic
36C2×#6717C2211yescharacteristic
37C2×#6717C2211yescharacteristic
38C2×#6717C2211yescharacteristic
39C2×#6717C2211yescharacteristic
40C2×#6717C2211yescharacteristic
41#91826—21no—
42#91819C2211yescharacteristic
43#91813C2211yescharacteristic
44C2×#6710C2211yescharacteristic, complemented
45C22×C3⋊#168C2211yescharacteristic
46#91783—21no—
47#91773—21no—
48C22⋊C4×D15—21no—
49#91764C2211yescharacteristic
50C4×D60C2211yescharacteristic
51#91119C2211yescharacteristic, complemented
52#91119C2211yescharacteristic, complemented
53#91119C2211yescharacteristic, complemented
54#91114C2211yescharacteristic
55#91114C2211yescharacteristic, complemented
56#91094C2211yescharacteristic, complemented
57#91093C2211yescharacteristic
58#91093C2211yescharacteristic
59#91091C2211yescharacteristic, complemented
60C4⋊(C3⋊#168)C2211yescharacteristic, complemented
61#91087C2211yescharacteristic, complemented
62#83559—51nomaximal, Hall
63C5×D4×Q8D311yescharacteristic, complemented
64C2×#4088—31no—
65C22×#688—31no—
66#65884—31no—
67#65517—31no—
68#65516—31no—
69#65375—31no—
70#65372—31no—
71#65340—31no—
72#65338—31no—
73#65336—31no—
74#65335—31no—
75#65317—31no—
76#65315—31no—
77#65300—31no—
78C23×D15—21no—
79C2×C3×C5×Q8—21no—
80C2×C3×C5×Q8—21no—
81C2×C3×C5×Q8—22no—
82C2×C3×C5×Q8—22no—
83C2×C3×C5×Q8—41no—
84C2×C3×C5×Q8—41no—
85C2×C3×C5×Q8C2311yescharacteristic
86C2×C3×C5×Q8C2311yescharacteristic
87C2×C3×C5×Q8C2311yescharacteristic
88C2×C3×C5×D4D411yescharacteristic
89C22×C3×C4×C5—21no—
90C22×C3×C4×C5—21no—
91C22×C3×C4×C5C2311yescharacteristic
92C22×C3×C4×C5C2311yescharacteristic
93C2×#1220—21no—
94C2×#1220—21no—
95#6817—22no—
96#6817—41no—
97C2×D60—22no—
98C2×D60—21no—
99C2×D60—41no—
100C2×D60C2311yescharacteristic
101C2×D60C2311yescharacteristic
102C2×C4×D15—21no—
103C2×C4×D15—21no—
104C2×Dic30C2311yescharacteristic
105C3×C5×C4⋊C4—21no—
106C3×C5×C4⋊C4—21no—
107C3×C5×C4⋊C4—21no—
108C3×C5×C4⋊C4—21no—
109C3×C5×C4⋊C4—21no—
110C3×C5×C4⋊C4D411yescharacteristic
111C3×C5×C4⋊C4C2311yescharacteristic
112C3×C5×C22⋊C4—21no—
113C3×C5×C22⋊C4—21no—
114C3×C5×C22⋊C4D411yescharacteristic
115C3×C5×C22⋊C4D411yescharacteristic
116C3×C42×C5—21no—
117C3×C42×C5C2311yescharacteristic
118#6719—21no—
119#6718—22no—
120#6718—22no—
121#6718—41no—
122#6717—22no—
123#6717—22no—
124#6717—22no—
125#6717—22no—
126#6717—41no—
127#6717D414yescomplemented
128#6714—21no—
129#6714—21no—
130#6714—21no—
131#6714—21no—
132C4⋊Dic15C2311yescharacteristic
133#6712—21no—
134#6710—22no—
135C2×C3⋊#168—22no—
136C2×C3⋊#168C2311yescharacteristic
137C2×C3⋊#168C2311yescharacteristic
138C2×C3⋊#168C2311yescharacteristic
139C2×C3⋊#168C2311yescharacteristic
140C3×D4×Q8D511yescharacteristic, complemented
141C2×#942—51no—
142C22×#215—51no—
143#5550—51no—
144#5228—51no—
145#5227—51no—
146#5086—51no—
147#5083—51no—
148#5051—51no—
149#5049—51no—
150#5047—51no—
151#5046—51no—
152#5028—51no—
153#5026—51no—
154#5011—51no—
155C22×C5×Q8C2×D311yescharacteristic
156C22×C5×Q8C2×D311yescharacteristic, complemented
157C2×#709—31no—
158C22×D20—31no—
159C5×C4⋊Q8—21no—
160C5×C4⋊Q8C2×D311yescharacteristic, complemented
161C5×C22⋊Q8—21no—
162C5×C22⋊Q8—21no—
163C5×C22⋊Q8C2×D311yescharacteristic
164C5×C22⋊Q8C2×D311yescharacteristic, complemented
165C4×C5×Q8C2×D311yescharacteristic, complemented
166C4×C5×D4—21no—
167C4×C5×D4C2×D311yescharacteristic
168C2×#689—31no—
169C2×#689—31no—
170C2×#689—31no—
171#4088—64no—
172C2×#688—31no—
173C2×#688—31no—
174C2×#688—31no—
175C2×#688—31no—
176C2×#688—31no—
177C2×#688—31no—
178C2×#688—64no—
179#4083—61no—
180#4076—31no—
181#4070—31no—
182C2×#681—31no—
183C22×#168—31no—
184#4040—61no—
185#4030—61no—
186D5×C22⋊C4—61no—
187#4021—31no—
188C4×D20—31no—
189#3967—31no—
190#3967—31no—
191#3967—31no—
192C22⋊#168—31no—
193C22⋊#168—31no—
194#3942—31no—
195#3941—31no—
196#3941—31no—
197#3939—31no—
198C4⋊#168—31no—
199#3935—31no—
200#3266—151noSylow
201C23×C3×C5C2×D411yescharacteristic
202C23×C3×C5C2×D411yescharacteristic
203C22×D15—21no—
204C22×D15—21no—
205C22×D15—42no—
206C22×D15—42no—
207C22×D15—81no—
208C3×C5×Q8—21no—
209C3×C5×Q8—21no—
210C3×C5×Q8—21no—
211C3×C5×Q8—21no—
212C3×C5×Q8—21no—
213C3×C5×Q8—42no—
214C3×C5×Q8—42no—
215C3×C5×Q8C2×D412yes—
216C3×C5×D4—22no—
217C2×C3×C4×C5—21no—
218C2×C3×C4×C5—21no—
219C2×C3×C4×C5—21no—
220C2×C3×C4×C5—21no—
221C2×C3×C4×C5—21no—
222C2×C3×C4×C5—21no—
223C2×C3×C4×C5—21no—
224C2×C3×C4×C5—21no—
225C2×C3×C4×C5—42no—
226C2×C3×C4×C5—42no—
227C2×C3×C4×C5C2×D411yescharacteristic
228C2×C3×C4×C5C2×D411yescharacteristic
229C2×C3×C4×C5C2×D411yescharacteristic
230C2×C3×C4×C5C2×D411yescharacteristic
231C2×C3×C4×C5C2411yescharacteristic
232#1220—42no—
233#1220—81no—
234C2×Dic15—21no—
235C2×Dic15—21no—
236D60—21no—
237D60—21no—
238D60—21no—
239D60—42no—
240D60C2×D412yes—
241C4×D15—42no—
242C4×D15—81no—
243Dic30—21no—
244Dic30—21no—
245C3⋊#168—21no—
246C3⋊#168—21no—
247C3⋊#168—21no—
248C3⋊#168C2×D412yes—
249C22×C3×Q8C2×D511yescharacteristic
250C22×C3×Q8C2×D511yescharacteristic, complemented
251C2×#235—51no—
252C22×D12—51no—
253C3×C4⋊Q8—21no—
254C3×C4⋊Q8C2×D511yescharacteristic, complemented
255C3×C22⋊Q8—21no—
256C3×C22⋊Q8—21no—
257C3×C22⋊Q8C2×D511yescharacteristic
258C3×C22⋊Q8C2×D511yescharacteristic, complemented
259C3×C4×Q8C2×D511yescharacteristic, complemented
260C3×C4×D4—21no—
261C3×C4×D4C2×D511yescharacteristic
262C2×#216—51no—
263C2×#216—51no—
264C2×#216—51no—
265#942—104no—
266C2×#215—51no—
267C2×#215—51no—
268C2×#215—51no—
269C2×#215—51no—
270C2×#215—51no—
271C2×#215—51no—
272C2×#215—104no—
273#937—101no—
274#930—51no—
275#924—51no—
276C2×#208—51no—
277C22×C3⋊C8—51no—
278#894—101no—
279#884—101no—
280D3×C22⋊C4—101no—
281#875—51no—
282C4×D12—51no—
283#835—51no—
284#835—51no—
285#835—51no—
286#830—51no—
287#830—51no—
288#810—51no—
289#809—51no—
290#809—51no—
291#807—51no—
292C4⋊(C3⋊C8)—51no—
293#803—51no—
294C23×D5—61no—
295C2×C5×Q8—21no—
296C2×C5×Q8—21no—
297C2×C5×Q8—22no—
298C2×C5×Q8—22no—
299C2×C5×Q8—41no—
300C2×C5×Q8—41no—
301C2×C5×Q8C22×D311yescharacteristic
302C2×C5×Q8C22×D311yescharacteristic
303C2×C5×Q8C22×D311yescharacteristic
304C2×C5×D4#6711yescharacteristic
305C22×C4×C5—21no—
306C22×C4×C5—21no—
307C22×C4×C5C22×D311yescharacteristic
308C22×C4×C5C22×D311yescharacteristic
309C2×C22⋊D5—61no—
310C2×C22⋊D5—61no—
311#709—62no—
312#709—121no—
313C2×D20—31no—
314C2×D20—31no—
315C2×D20—62no—
316C2×D20—61no—
317C2×D20—121no—
318C2×C4×D5—61no—
319C2×C4×D5—61no—
320C2×Dic10—31no—
321C5×C4⋊C4—21no—
322C5×C4⋊C4—21no—
323C5×C4⋊C4—21no—
324C5×C4⋊C4—21no—
325C5×C4⋊C4—21no—
326C5×C4⋊C4#6711yescharacteristic
327C5×C4⋊C4C22×D311yescharacteristic
328C5×C22⋊C4—21no—
329C5×C22⋊C4—21no—
330C5×C22⋊C4#6711yescharacteristic
331C5×C22⋊C4#6711yescharacteristic
332C42×C5—21no—
333C42×C5C22×D311yescharacteristic
334C22⋊Dic5—61no—
335#689—62no—
336#689—62no—
337#689—121no—
338#688—34no—
339#688—62no—
340#688—62no—
341#688—62no—
342#688—62no—
343#688—121no—
344#685—61no—
345#685—61no—
346#685—61no—
347#685—61no—
348C4⋊Dic5—31no—
349#683—61no—
350#681—62no—
351C2×#168—31no—
352C2×#168—31no—
353C2×#168—31no—
354C2×#168—31no—
355C2×#168—62no—
356C2×#137—151no—
357C22×SD16—151no—
358D4×Q8D1511yescharacteristic, complemented
359#546—151no—
360#497—151no—
361#468—151no—
362#467—151no—
363#464—151no—
364#461—151no—
365#452—151no—
366#451—151no—
367#450—151no—
368#448—151no—
369#440—151no—
370#435—151no—
371C22×C3×C5—21no—
372C22×C3×C5—21no—
373C22×C3×C5—21no—
374C22×C3×C5—21no—
375C22×C3×C5—21no—
376C22×C3×C5#13712yescomplemented
377C22×C3×C5C22×D411yescharacteristic
378C2×D15—22no—
379C2×D15—41no—
380C2×D15—41no—
381C2×D15—41no—
382C2×D15—41no—
383C2×D15—41no—
384C2×D15—84no—
385C3×C4×C5—21no—
386C3×C4×C5—21no—
387C3×C4×C5—22no—
388C3×C4×C5—21no—
389C3×C4×C5—21no—
390C3×C4×C5—41no—
391C3×C4×C5—41no—
392C3×C4×C5—41no—
393C3×C4×C5C22×D411yescharacteristic
394C3×C4×C5H(5,𝔽2)11yescharacteristic
395Dic15—41no—
396Dic15—41no—
397C23×D3—101no—
398C2×C3×Q8—21no—
399C2×C3×Q8—21no—
400C2×C3×Q8—22no—
401C2×C3×Q8—22no—
402C2×C3×Q8—41no—
403C2×C3×Q8—41no—
404C2×C3×Q8C22×D511yescharacteristic
405C2×C3×Q8C22×D511yescharacteristic
406C2×C3×Q8C22×D511yescharacteristic
407C2×C3×D4C22⋊D511yescharacteristic
408C22×C3×C4—21no—
409C22×C3×C4—21no—
410C22×C3×C4C22×D511yescharacteristic
411C22×C3×C4C22×D511yescharacteristic
412C2×#67—101no—
413C2×#67—101no—
414#235—102no—
415#235—201no—
416C2×D12—51no—
417C2×D12—51no—
418C2×D12—102no—
419C2×D12—101no—
420C2×D12—201no—
421C2×C4×D3—101no—
422C2×C4×D3—101no—
423C2×Dic6—51no—
424C3×C4⋊C4—21no—
425C3×C4⋊C4—21no—
426C3×C4⋊C4—21no—
427C3×C4⋊C4—21no—
428C3×C4⋊C4—21no—
429C3×C4⋊C4C22⋊D511yescharacteristic
430C3×C4⋊C4C22×D511yescharacteristic
431C3×C22⋊C4—21no—
432C3×C22⋊C4—21no—
433C3×C22⋊C4C22⋊D511yescharacteristic
434C3×C22⋊C4C22⋊D511yescharacteristic
435C3×C42—21no—
436C3×C42C22×D511yescharacteristic
437#217—101no—
438#216—102no—
439#216—102no—
440#216—201no—
441#215—54no—
442#215—102no—
443#215—102no—
444#215—102no—
445#215—102no—
446#215—201no—
447(C2×D3)⋊C4—101no—
448(C2×D3)⋊C4—101no—
449(C2×D3)⋊C4—101no—
450(C2×D3)⋊C4—101no—
451C4⋊Dic3—51no—
452Dic3⋊C4—101no—
453#208—102no—
454C2×C3⋊C8—51no—
455C2×C3⋊C8—51no—
456C2×C3⋊C8—51no—
457C2×C3⋊C8—51no—
458C2×C3⋊C8—102no—
459C23×C5C2×#6711yescharacteristic
460C23×C5C2×#6711yescharacteristic
461C22×D5—61no—
462C22×D5—61no—
463C22×D5—122no—
464C22×D5—122no—
465C22×D5—241no—
466C5×Q8—21no—
467C5×Q8—21no—
468C5×Q8—21no—
469C5×Q8—21no—
470C5×Q8—21no—
471C5×Q8—42no—
472C5×Q8—42no—
473C5×Q8D3×D412yes—
474C5×D4—22no—
475C2×C4×C5—21no—
476C2×C4×C5—21no—
477C2×C4×C5—21no—
478C2×C4×C5—21no—
479C2×C4×C5—21no—
480C2×C4×C5—21no—
481C2×C4×C5—21no—
482C2×C4×C5—21no—
483C2×C4×C5—42no—
484C2×C4×C5—42no—
485C2×C4×C5C2×#6711yescharacteristic
486C2×C4×C5C2×#6711yescharacteristic
487C2×C4×C5C2×#6711yescharacteristic
488C2×C4×C5C2×#6711yescharacteristic
489C2×C4×C5C23×D311yescharacteristic
490C22⋊D5—122no—
491C22⋊D5—241no—
492C2×Dic5—61no—
493C2×Dic5—61no—
494D20—32no—
495D20—61no—
496D20—61no—
497D20—61no—
498D20—122no—
499C4×D5—122no—
500C4×D5—241no—
501Dic10—61no—
502Dic10—61no—
503#168—32no—
504#168—61no—
505#168—61no—
506#168—61no—
507C2×#41—151no—
508C22×Q8C2×D1511yescharacteristic
509C22×Q8C2×D1511yescharacteristic, complemented
510C22×D4—151no—
511#137—304no—
512C2×Q16—151no—
513C2×Q16—151no—
514C2×Q16—151no—
515C2×SD16—151no—
516C2×SD16—151no—
517C2×SD16—151no—
518C2×SD16—151no—
519C2×SD16—151no—
520C2×SD16—151no—
521C2×SD16—304no—
522C2×M16—151no—
523C22×C8—151no—
524C4⋊Q8—21no—
525C4⋊Q8C2×D1511yescharacteristic, complemented
526#124—151no—
527#123—301no—
528C22⋊Q8—21no—
529C22⋊Q8—21no—
530C22⋊Q8—151no—
531C22⋊Q8C2×D1511yescharacteristic
532C22⋊Q8C2×D1511yescharacteristic, complemented
533#121—151no—
534#121—301no—
535#120—301no—
536C4×Q8C2×D1511yescharacteristic, complemented
537C4×D4—21no—
538C4×D4—151no—
539C4×D4C2×D1511yescharacteristic
540C2×C22⋊C4—301no—
541#107—151no—
542C4⋊C8—151no—
543#103—151no—
544#103—151no—
545#103—151no—
546#103—151no—
547#102—151no—
548#102—151no—
549C22⋊C8—151no—
550C22⋊C8—151no—
551#97—151no—
552C2×C3×C5—22no—
553C2×C3×C5—41no—
554C2×C3×C5D4211yescharacteristic
555C2×C3×C5C2×#13711yescharacteristic
556C2×C3×C5#57711yescharacteristic
557D15—42no—
558D15—81no—
559C23×C3C2×C22⋊D511yescharacteristic
560C23×C3C2×C22⋊D511yescharacteristic
561C22×D3—101no—
562C22×D3—101no—
563C22×D3—202no—
564C22×D3—202no—
565C22×D3—401no—
566C3×Q8—21no—
567C3×Q8—21no—
568C3×Q8—21no—
569C3×Q8—21no—
570C3×Q8—21no—
571C3×Q8—42no—
572C3×Q8—42no—
573C3×Q8D4×D512yes—
574C3×D4—22no—
575C2×C3×C4—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—42no—
584C2×C3×C4—42no—
585C2×C3×C4C2×C22⋊D511yescharacteristic
586C2×C3×C4C2×C22⋊D511yescharacteristic
587C2×C3×C4C2×C22⋊D511yescharacteristic
588C2×C3×C4C2×C22⋊D511yescharacteristic
589C2×C3×C4C23×D511yescharacteristic
590#67—202no—
591#67—401no—
592C2×Dic3—101no—
593C2×Dic3—101no—
594D12—52no—
595D12—101no—
596D12—101no—
597D12—101no—
598D12—202no—
599C4×D3—202no—
600C4×D3—401no—
601Dic6—101no—
602Dic6—101no—
603C3⋊C8—52no—
604C3⋊C8—101no—
605C3⋊C8—101no—
606C3⋊C8—101no—
607C22×C5—21no—
608C22×C5—21no—
609C22×C5—21no—
610C22×C5—21no—
611C22×C5—21no—
612C22×C5#94212yescomplemented
613C22×C5C22×#6711yescharacteristic
614C2×D5—62no—
615C2×D5—121no—
616C2×D5—121no—
617C2×D5—121no—
618C2×D5—121no—
619C2×D5—121no—
620C2×D5—244no—
621C4×C5—21no—
622C4×C5—21no—
623C4×C5—22no—
624C4×C5—21no—
625C4×C5—21no—
626C4×C5—41no—
627C4×C5—41no—
628C4×C5—41no—
629C4×C5C2×D3×D411yescharacteristic
630C4×C5#100411yescharacteristic
631Dic5—121no—
632Dic5—121no—
633C24—301no—
634#41—302no—
635#41—601no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—22no—
639C2×Q8—22no—
640C2×Q8—41no—
641C2×Q8—41no—
642C2×Q8—151no—
643C2×Q8C22×D1511yescharacteristic
644C2×Q8C22×D1511yescharacteristic
645C2×Q8C22×D1511yescharacteristic
646C2×D4—151no—
647C2×D4—151no—
648C2×D4—302no—
649C2×D4—301no—
650C2×D4—301no—
651C2×D4—301no—
652C2×D4—601no—
653C2×D4#122011yescharacteristic
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—301no—
657C22×C4—301no—
658C22×C4C22×D1511yescharacteristic
659C22×C4C22×D1511yescharacteristic
660Q16—302no—
661Q16—302no—
662Q16—601no—
663SD16—154no—
664SD16—302no—
665SD16—302no—
666SD16—302no—
667SD16—302no—
668SD16—601no—
669M16—302no—
670C2×C8—151no—
671C2×C8—151no—
672C2×C8—151no—
673C2×C8—151no—
674C2×C8—302no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—151no—
681C4⋊C4—301no—
682C4⋊C4#122011yescharacteristic
683C4⋊C4C22×D1511yescharacteristic
684C22⋊C4—21no—
685C22⋊C4—21no—
686C22⋊C4—301no—
687C22⋊C4—301no—
688C22⋊C4—301no—
689C22⋊C4—301no—
690C22⋊C4—301no—
691C22⋊C4#122011yescharacteristic
692C22⋊C4#122011yescharacteristic
693C42—21no—
694C42C22×D1511yescharacteristic
695C3×C5#326611yescharacteristic, complemented, Hall
696C22×C3—21no—
697C22×C3—21no—
698C22×C3—21no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3#408812yescomplemented
702C22×C3C22×C22⋊D511yescharacteristic
703C2×D3—102no—
704C2×D3—201no—
705C2×D3—201no—
706C2×D3—201no—
707C2×D3—201no—
708C2×D3—201no—
709C2×D3—404no—
710C3×C4—21no—
711C3×C4—21no—
712C3×C4—22no—
713C3×C4—21no—
714C3×C4—21no—
715C3×C4—41no—
716C3×C4—41no—
717C3×C4—41no—
718C3×C4C2×D4×D511yescharacteristic
719C3×C4#414411yescharacteristic
720Dic3—201no—
721Dic3—201no—
722C2×C5—22no—
723C2×C5—41no—
724C2×C5D4×#6711yescharacteristic
725C2×C5C2×#94211yescharacteristic
726C2×C5#583711yescharacteristic
727D5—122no—
728D5—241no—
729C23—301no—
730C23—301no—
731C23—602no—
732C23—602no—
733C23—1201no—
734C23C2×#122011yescharacteristic
735C23C2×#122011yescharacteristic
736Q8—21no—
737Q8—21no—
738Q8—21no—
739Q8—21no—
740Q8—21no—
741Q8—42no—
742Q8—42no—
743Q8—301no—
744Q8—301no—
745Q8D4×D1512yes—
746D4—22no—
747D4—152no—
748D4—301no—
749D4—301no—
750D4—301no—
751D4—602no—
752D4—602no—
753D4—1201no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—301no—
765C2×C4—301no—
766C2×C4—602no—
767C2×C4—1201no—
768C2×C4C2×#122011yescharacteristic
769C2×C4C2×#122011yescharacteristic
770C2×C4C2×#122011yescharacteristic
771C2×C4C2×#122011yescharacteristic
772C2×C4C23×D1511yescharacteristic
773C8—152no—
774C8—301no—
775C8—301no—
776C8—301no—
777C2×C3—22no—
778C2×C3—41no—
779C2×C3D4×C22⋊D511yescharacteristic
780C2×C3C2×#408811yescharacteristic
781C2×C3#6617111yescharacteristic
782D3—202no—
783D3—401no—
784C5#8355911yescharacteristic, complemented, Sylow
785C22—21no—
786C22—21no—
787C22—21no—
788C22—21no—
789C22—21no—
790C22—302no—
791C22—601no—
792C22—601no—
793C22—601no—
794C22—601no—
795C22—601no—
796C22—1204no—
797C22#9183112yescomplemented
798C22C22×#122011yescharacteristic
799C4—21no—
800C4—21no—
801C4—22no—
802C4—21no—
803C4—21no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—601no—
808C4—601no—
809C4C2×D4×D1511yescharacteristic
810C4#9209511yescharacteristic
811C3#1061529011yescharacteristic, complemented, Sylow
812C2—22no—
813C2—41no—
814C2—602no—
815C2—1201no—
816C2D4×#122011yescharacteristic
817C2C2×#9183111yescharacteristic
818C2#1175659611yescharacteristic
subgroupG/H
centerC22C22×#1220
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C23×D15
FittingC3×C5×D4×Q8C2
socleC22×C3×C5C22×D4
prime radical#11756309C2
hypercenterD4×Q8D15
hypocenterC3×C5#3266
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×D4 ◁ D4×Q8

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×C5×D4×Q8C2semidirect
2. C2×#91831C2semidirect
3. C22×#6717C2semidirect
5. #11751329C2semidirect
6. #11751328C2semidirect
7. #11751187C2semidirect
8. #11751184C2semidirect
9. #11751152C2semidirect
10. #11751150C2semidirect
11. #11751148C2semidirect
12. #11751147C2semidirect
13. #11751129C2semidirect
14. #11751127C2semidirect
15. #11751112C2semidirect
18. C22×C3×C5×Q8C22semidirect
22. C3×C5×C4⋊Q8C22semidirect
26. C3×C5×C22⋊Q8C22semidirect
27. C3×C4×C5×Q8C22semidirect
30. C2×#6718C22semidirect
31. C2×#6718C22semidirect
32. C2×#6718C22semidirect
44. C2×#6710C22semidirect
51. #91119C22semidirect
52. #91119C22semidirect
53. #91119C22semidirect
55. #91114C22semidirect
56. #91094C22semidirect
59. #91091C22semidirect
60. C4⋊(C3⋊#168)C22semidirect
61. #91087C22semidirect
63. C5×D4×Q8D3semidirect
127. #6717D4semidirect
140. C3×D4×Q8D5semidirect
156. C22×C5×Q8C2×D3semidirect
160. C5×C4⋊Q8C2×D3semidirect
164. C5×C22⋊Q8C2×D3semidirect
165. C4×C5×Q8C2×D3semidirect
250. C22×C3×Q8C2×D5semidirect
254. C3×C4⋊Q8C2×D5semidirect
258. C3×C22⋊Q8C2×D5semidirect
259. C3×C4×Q8C2×D5semidirect
358. D4×Q8D15semidirect
376. C22×C3×C5#137semidirect
509. C22×Q8C2×D15semidirect
525. C4⋊Q8C2×D15semidirect
532. C22⋊Q8C2×D15semidirect
536. C4×Q8C2×D15semidirect
612. C22×C5#942semidirect
695. C3×C5#3266semidirect
701. C22×C3#4088semidirect
784. C5#83559semidirect
797. C22#91831semidirect
811. C3#10615290semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×C5×D4×Q82
C2×#918312
C22×#67172
#117563092
#117513292
#117513282
#117511872
#117511842
#117511522
#117511502
#117511482
#117511472
#117511292
#117511272
#117511122
#106152903
#835595